Then you are trying to run it as root. postfix won't allow you to do that.

> When my script is called by postfix, I get permission errors when
> writing certain file locations. If I run the same script as
> nobody:nobody via sudo, those errors do not occur.
>

That doesn't make any sense.

> I am not using chroot for any part of postfix. It seems like some kind
> of group restriction is being layered on top. Through experimentation
> I've found my script, when called by postfix and running as
> nobody:nobody:
> 1. Can write to locations that are writable by all users.
>
As expected.
> 2. Can write to locations that are owner-writable and owned by nobody
>
As expected.
> 3. Can write to locations that are group-writable and are set to group nobody.
>
As expected.
> 4. Cannot write to locations that are group-writable and set to some
> other group - even if the user nobody is part of the relevant group.
>
As expected.
> I don't see anything in pipe's man page indicating this restriction,
>

I quote:

*user*=/username/:/groupname/
Execute the external command with the user ID and
group ID of the specified/username/._/*The software
*/_/* */_/* refuses to execute commands with root privileges,
*/_/* */_/* or with the privileges of the mail system owner.*/_ If
/groupname/ is specified, the corresponding group ID
is used instead of the group ID of/username/.

Emphasis mine.

And just in case you're using local(8) with external command delivery
instead:

*DELIVERY RIGHTS*
Deliveries to external files and external commands are
made with the rights of the receiving user on whose behalf
the delivery is made.

Never, not in any conceivable situation, does postfix execute external
commands as nobody:nobody - unless you're trying to execute as root, and
default_privs is actually SET to nobody:nobody.